Abstract
For linear (control) systems on infinite-dimensional state spaces with finite-dimensional unstable subspace, this paper introduces the concepts of topological entropy and invariance entropy. For linear dynamical systems on Banach spaces, described by a strongly continuous semigroup, the topological entropy is given by the sum of the real parts of the unstable eigenvalues of the infinitesimal generator. An application is provided by computing the topological entropy of delay equations and of a parabolic partial differential equation. Furthermore, the invariance entropy for infinite-dimensional linear control systems is equal to the topological entropy of the homogeneous equation and so it is also described by the eigenvalues of the infinitesimal generator.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
